Perfect periodic sequences for nonlinear Wiener filters

A periodic sequence is defined as a perfect periodic sequence for a certain nonlinear filter if the cross-correlation between any two of the filter basis functions, estimated over a period, is zero. Using a perfect periodic sequence as input signal, an unknown nonlinear system can be efficiently identified with the cross-correlation method. Moreover, the basis functions that guarantee the most compact representation according to some information criterion can also be easily estimated. Perfect periodic sequences have already been developed for even mirror Fourier, Legendre and Chebyshev nonlinear filters. In this paper, we show they can be developed also for nonlinear Wiener filters. Their development is non-trivial and differs from that of the other nonlinear filters, since Wiener filters have orthogonal basis functions for white Gaussian input signals. Experimental results highlight the usefulness of the proposed perfect periodic sequences in comparison with the Gaussian input signals commonly used for Wiener filter identification.